In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold and that they are stable under perturbations of the map. This generalizes certain ideas of persistent homology to higher dimensions.

中文翻译：

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持久的本地系统

在本文中，我们给出了映射到流形的纤维同源性的下限。使用新的层理论方法，我们表明这些下界在流形的整个开放集上持续存在，并且它们在地图的扰动下是稳定的。这将某些持久同源性的想法推广到更高的维度。